OCEAN TEMPEEATURES 



389 



In case w is constant, assume for the form of the solution 



6 = fM tan at + f 2 (y)eo S at + f s (y)x + ft(y)+6 i (140) 



where ^ is independent of t and x. Substitute this expression in 

 equation (139), thus obtaining the following equations: 



(sin /,(*) - k. 

 (cos aO [ -a/, (y) + B 



ay 



= 

 (142) 

 =0 (143) 



(144) 



in which # is regarded as a constant. 



In case of no vertical velocity the variation of (6 O t ) with respect 

 to time is small compared to its mean value, which is independent of 

 the time (p. 344). Therefore, assuming this to be true for the present 

 case, a good approximation would result if the constant part were 

 multiplied by the correct factor fe t e" 6ij/ and the variable part by an 

 average value k. Making this change in equations (141) to (144) 

 we have the much simpler ones 



(145) 

 (146) 



(147) 



From equations (145) and (146) 



(149) 



where 



= k ^& and tan 60=:^-. 



